As to the prior art, reference is made to the publication WO 98/53666 disclosing a sawing unit, in which the second machine element performing the second partial work performance consists of the combination of a toothed rack in a cylinder-piston mechanism operated by a pressurized medium, fixed to the cylinder-piston mechanism and arranged to be movable in its longitudinal direction, and a toothed rim fixed at the end of the sawing unit, in connection with the flange of the saw chain and in cooperation with the rack. The sawing unit is functional as such, and it provides an even moment and a steady speed during the sawing performance. However, the sawing unit presented in said publication WO 98/53666 is, primarily due to its overall principle of operation, massive and bulky in its outer dimensions, wherein it is difficult to place, for example, in connection with the harvester head of a forest machine. On the other hand, the construction of the sawing unit is relatively complex, wherein it has a high price.